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Dipole vector associated with charges

  • #1

Homework Statement


Problem attached in Dipole.Jpg


Homework Equations





The Attempt at a Solution


I am fine with Part A of the problem. Im just trying to understand what part B is asking. Are they asking what is the magnitude and direction of the dipole vector associated with charges q1 and q1 at point P? It is not clear to me. If so they would be asking about the dipole vector associated with the plane that bisects the dipole so I would use E(dipole)=-(1/4pi episolonnot) P/r^3? P is dipole moment
So really I would use -kqs/r^3 where s is distance between charges.
I can't imagine what else the problem is asking.
Another question would be is the q in the above equation the sum of q1 and q2?
Any help would be much appreciated!
Thanks in advanced!!!
 

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  • #2
Charles Link
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I would avoid trying to solve this one with dipole formulas. The dipole formulas work for ## r>>d ##. I don't know that they work at close range. The simplest way to solve it is just to use vectors and the inverse square law.
 
  • #3
Orodruin
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They are asking for the dipole moment associated with the two charges. The dipole moment relative to a point is given by summing the charge multiplied by the position vector over all charges. For an overall neutral charge configuration, this does not depend on the point. The dipole moment is not the electric field.

I would avoid trying to solve this one with dipole formulas. The dipole formulas work for ## r>>d ##. I don't know that they work at close range. The simplest way to solve it is just to use vectors and the inverse square law.
You cannot solve B without using an expression for the dipole moment since the problem asks you to find the dipole moment. This part of the problem has nothing to do with the part of finding the field at p.
 
  • #4
Charles Link
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I was looking ahead to (d) which the OP seems to be referring to, by mentioning an electric field proportional to ## \frac{1}{r^3} ##. ## \\ ## (b) amd (c) are relatively simple, and I think it is misleading the student to try to get them to use these results to solve (d) in this problem.
 
  • #5
Orodruin
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The OP is asking about part B, not part D.

Im just trying to understand what part B is asking.
The issue is understanding that the dipole moment is not the electric field, but what I described in #3.
 
  • #6
SammyS
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Homework Statement


Problem attached in Dipole.Jpg
dipole-jpg.jpg

Homework Equations



The Attempt at a Solution


I am fine with Part A of the problem. Im just trying to understand what part B is asking. Are they asking what is the magnitude and direction of the dipole vector associated with charges q1 and q1 at point P? It is not clear to me. If so they would be asking about the dipole vector associated with the plane that bisects the dipole so I would use E(dipole)=-(1/4pi episolonnot) P/r^3? P is dipole moment
So really I would use -kqs/r^3 where s is distance between charges.
I can't imagine what else the problem is asking.
Another question would be is the q in the above equation the sum of q1 and q2?
Any help would be much appreciated!
Thanks in advanced!!!
Part (b) asks a question about a dipole vector but says nothing about "at point P".
Part (c) also asks a question about a dipole vector..

Answer Parts (a) and (d) using Coulomb's Law, for electric field. These parts have nothing to do with dipoles.
 

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  • #8
Hmmm. I assume the dipole vector that is associated with the two charges in question (q1 &q2), will create an electric field at point P? Ive attached my logic "dipole problem.JPG"
 

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  • #9
I was looking ahead to (d) which the OP seems to be referring to, by mentioning an electric field proportional to ## \frac{1}{r^3} ##. ## \\ ## (b) amd (c) are relatively simple, and I think it is misleading the student to try to get them to use these results to solve (d) in this problem.
Yes I believe I was mixing equations up from the book, my notes, and my head. I will look at D now and see if I can make sense of that one. Thanks!
 
  • #10
Charles Link
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A detailed analysis of the dipole formulas show that they are intended for distances ## r>>d ## and will not work at close range. In this sense, in this combination of 4 questions, (b) and (c) are really unrelated and are misleading you. The results in (b) and (c) can not be used to solve part (d).
 
  • #11
View attachment 230535

Part (b) asks a question about a dipole vector but says nothing about "at point P".
Part (c) also asks a question about a dipole vector..

Answer Parts (a) and (d) using Coulomb's Law, for electric field. These parts have nothing to do with dipoles.
Ahh, okay. I guess thats true. So
Hmmm. I assume the dipole vector that is associated with the two charges in question (q1 &q2), will create an electric field at point P? Ive attached my logic "dipole problem.JPG"
Okay, Just read some responses. So this is not correct then. Ill go back and read on what Dipole Vector means.
 
  • #12
SammyS
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  • #15
Charles Link
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To give you a quick introduction to it, the ## \frac{1}{r^3} ## behavior of electric and magnetic dipoles is actually very useful in analyzing some rather advanced E&M (electricity and magnetism) problems, and is used in the computation of the electric and/or magnetic fields at a distance from what are microscopic dipoles (with very small ## d ##). ## \\ ## In this problem, they are teaching you in parts (b) and (c) a couple of simple definitions, but nothing more than that. The ## \frac{1}{r^3} ## formulas do not apply at very close range=they do not give a correct result.
 
  • #16
SammyS
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Thanks for the link. Is it true that the statement " what is the magnitude and and direction of the dipole vector" is referring to the dipole moment? and If so it would be
P=Qa(-i) ?
For part (b): Yes .
 
  • #17
For part (b): Yes .
Okay, therefore part C would be:
P=2Qa(i)
 
  • #18
SammyS
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  • #19
Thanks everyone! appreciate the help :)
 

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